Experimental characterisation and transfer matrix modelling of first natural frequencies in axially graded fused deposition modelling-printed polylactic acid cantilevers with edge cracks

Beams with axially varying infill density produced by fused deposition modelling (FDM) offer a route to tailor vibration response through manufacturing parameters, but few studies combine experimental and analytical characterisation of such beams with edge defects. In this work, polylactic acid (PLA) cantilever beams were fabricated by FDM with three axial infill distributions, uniform 50%, ascending 10% to 100%, and descending 100% to 10% from fixed to free end and tested with single-edge notches of depth 0 to 2.5 mm at the fixed end, giving 18 cracked-beam configurations. A separate set of 13 specimens, in which a 14 mm wide 10% infill segment was translated along an otherwise uniform 50% beam, served as an independent validation set that was not used in calibration. First natural frequencies were extracted from impulse-excitation measurements processed by three complementary methods (amplitude spectrum, power spectrum, time-domain peak counting), with a mean impulse-to-impulse standard deviation of 0.04 Hz. An analytical model combining a phenomenological linear constitutive law, the transfer matrix method, a Tada-Paris-Irwin rotational spring at the notch, and a point tip mass representing the accelerometer was calibrated against the 18-configuration cracked-beam dataset. Calibration converged to α E = 0.476 and α ρ = 0.522 with a 0.71 Hz RMSE; a profile-likelihood analysis showed both parameters are practically identifiable within the adopted model, dataset and reference properties E s and ρ s . Applied without re-fitting to the 13 segment-position specimens, the model reproduces all 31 configurations with a 4.0% mean absolute error, placing 28 within a ± 8% envelope.